Polynomials/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. Tim and Moby are on their hands and knees on a lawn. They are measuring an area of dirt to plant a garden. TIM: Okay, this side looks like it's about... Moby lets go of his end of the tape measure. It snaps back into the end Tim is holding. TIM: How are we supposed to measure this garden if you keep doing that? A letter appears on-screen. Text reads as Tim narrates: Dear Tim and Moby, can you tell me the difference between monomials and polynomials? From: Jeff. TIM: Sure. Polynomials are the mathematical expressions that include one or more parts, called terms. Onscreen, an expression appears, reading, x, plus 2x, squared minus 3x, to the third power. A label reads, polynomials. Another label reads, terms. TIM: A term is just a number, like the number 7, a variable, like x, or y, or a number multiplied by one or more variables, like 7 times x, or 7x. On-screen, three terms appear, reading, 7, x, and 7x. Moby beeps. TIM: That's right, Moby. Some polynomials have special names. A monomial, for instance, is just a polynomial with only one term. A label appears, reading, monomial. The monomial, y, appears, filling the screen. TIM: So, the y, you see here is a monomial--it has only one term. Same goes for this negative 2x, and that 4z, squared. On-screen, a monomial appears, reading, negative 2x. It changes to another monomial, 4z, squared. TIM: Binomials are polynomials with two terms, like 1 plus 5x. A binomial appears, reading, 1 plus 5x. A label reads, binomials. TIM: And trinomials like 6 plus 3y, plus y, squared have three terms. A trinomial appears, reading, 6 plus 3y, plus y, squared. A label reads, trinomials. Moby beeps. TIM: Good point. Any term with a variable in the denominator of a fraction or with a variable exponent is not a polynomial. On-screen, 5 over y, and 5 to the y, power appear. Moby shakes his head no and beeps. TIM: How do you get a polynomial? Well, here, let's make one! On-screen, an overhead of the garden appears. It is 6-sided, with sides of varying lengths. TIM: We haven’t been able to measure our garden, but we do know a little about its proportions. So, we can assign variables to each side. On-screen, a term appears along each side of the garden: x, x, y, y, z, and 2y. TIM: To find the perimeter, we’ll need to add up all those sides. That’s x, plus x, plus 2y, plus y, plus y, plus z. On-screen, a polynomial appears, reading, x, plus x, plus 2y, plus y, plus y, plus z. TIM: Simplifying gets us 2x, plus 4y, plus z. On-screen, the polynomial changes to read, 2x, plus 4y, plus z. TIM: That’s a polynomial all right, with three monomials added together. On-screen, 2x, 4y, and z, are each highlighted. Moby beeps. TIM: Sure, we can try another polynomial. What did you have in mind? Moby smiles. The polynomial 5x, squared plus xy, to the third power appears beside him. TIM: Ok then, 5 times x, squared plus x, times y, cubed is a polynomial. It’s made of two monomials so it’s actually a binomial. Since it contains exponents, it has what's called a degree. A label appears, reading, degree. TIM: You find the degree of a monomial by adding the exponents of the variables together. Remember that saying x, is really the same thing as saying x, to the first power. On-screen, the term xy, to the third power is highlighted. It changes to x, to the first power, time y, to the third power. TIM: So that monomial term has a degree of 4. The other monomial has a degree of 2. On-screen, the term 5x, squared is highlighted. TIM: We can ignore that 5 because it's a constant, and we're only looking for the exponents of variables. To find the degree of a whole polynomial, you just find the term with greatest degree. That's your polynomial's degree. In this case, it's 4. Moby beeps. TIM: Well, remember that a variable with no exponent is that variable to the first power. So if there are no exponents, the polynomial has a degree of 1. A polynomial appears, reading, 4x, plus y. Text below the polynomial reads, degree equals 1. TIM: There you go: polynomials! Now if you'll excuse us, we've got to get back to measuring the garden. On-screen, Tim holds up the tape measure. Moby’s arm reaches in from off-screen, and pulls the tape out. Tim watches with concern as Moby pull the tape out farther and farther. TIM: You wouldn’t… Moby beeps. TIM: Oh, no. Moby releases the tape. The screen goes black as we hear the tape rewind and snap loudly back into the case. TIM: Ow! Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts